Generalized Covering Groups and Direct Limits
arXiv:1103.5149
Abstract
M. R. R. Moghaddam (Monatsh. Math. 90 (1980) 37-43.) showed that the Baer invariant commutes with the direct limit of a directed system of groups. In this paper, using the generalization of Schur's formula for the structure of a -covering group for a Schur-Baer variety , we show that the structure of a -covering group commutes with the direct limit of a directed system, in some senses. It has a useful application in order to extend some known structures of -covering groups for several famous products of finitely many to an arbitrary family of groups.
22 pages